Details

sample260.0ms

Algorithm

intervals

Results

97.0ms	87×	body	1280	valid
87.0ms	30×	body	2560	valid
28.0ms	58×	body	640	valid
7.0ms	95×	body	80	valid
6.0ms	23×	body	320	valid
4.0ms	59×	body	80	nan
2.0ms	11×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	59	15
3	140	15
4	347	15
5	1514	15
done	5000	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.4b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

552.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
272.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
29.0ms	(pow (+ 1.0 (/ i n)) n)
518.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.9s

Counts

4 → 12

Calls

4 calls:

602.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
383.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
329.0ms	(pow (+ 1.0 (/ i n)) n)
547.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.2s

Counts

293 → 293

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	437	6469
1	1416	6211
done	5000	5919

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.1b	(* (pow i 2) (log 1.0))
19.6b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

36.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
486.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
34.0ms	(* (pow i 2) (log 1.0))
529.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series1.0s

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
362.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
287.0ms	(* (pow i 2) (log 1.0))
326.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify829.0ms

Counts

198 → 198

Iterations

Useful iterations: done (814.0ms)

Iter	Nodes	Cost
0	338	6829
1	1023	6655
done	5001	6143

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.1b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
10.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b	(* (pow i 2) (log 1.0))

rewrite933.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
11×	`associate-l`
10×	`pow1`
9×	`times-frac` `add-log-exp`
8×	`prod-exp`
6×	`log-prod` `cbrt-unprod`
5×	`associate-r`
4×	`unpow-prod-down` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `sum-log` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

38.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
404.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
461.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
24.0ms	(* (pow i 2) (log 1.0))

series974.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
360.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
231.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
308.0ms	(* (pow i 2) (log 1.0))

simplify1.8s

Counts

110 → 110

Iterations

Useful iterations: 2 (584.0ms)

Iter	Nodes	Cost
0	210	2896
1	548	2825
2	2739	2413
done	5000	2413

prune787.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.4b

localize82.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
7.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
8.4b	(* (/ 1 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
11.1b	(* (pow i 2) (log 1.0))

rewrite980.0ms

Algorithm

rewrite-expression-head

Rules

386×	`times-frac`
321×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
168×	`add-cube-cbrt`
104×	`add-exp-log`
94×	`cbrt-prod`
75×	`associate-r`
51×	`div-exp`
48×	`unswap-sqr`
45×	`associate-l`
38×	`unpow-prod-down`
33×	`prod-exp`
29×	`add-cbrt-cube`
22×	`associate-/r*`
13×	`unpow2` `sqr-pow`
12×	`cbrt-undiv`
10×	`pow-to-exp` `pow-exp` `div-inv`
9×	`rec-exp` `1-exp`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `log-pow` `flip--`

Counts

4 → 354

Calls

4 calls:

1.0ms	(cbrt i)
412.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
508.0ms	(* (/ 1 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
31.0ms	(* (pow i 2) (log 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

258.0ms	(cbrt i)
278.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
284.0ms	(* (/ 1 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
247.0ms	(* (pow i 2) (log 1.0))

simplify971.0ms

Counts

366 → 366

Iterations

Useful iterations: done (954.0ms)

Iter	Nodes	Cost
0	568	16027
1	1983	15372
done	5001	14254

prune2.3s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.4b

regimes762.0ms

Accuracy

46.4% (12.2b remaining)

Error of 23.4b against oracle of 11.1b and baseline of 34.0b

bsearch679.0ms

Steps

Iters	Range		Point
7	1.2646612175373838e-175	6.651096339829762e-174	2.1282130468923694e-175
9	-5.259837781237774e-183	-5.703441385580287e-192	-5.8053964764311714e-192
8	-1.1067698676223754e+18	-1112375351328255.6	-5.024789071547713e+16
7	-8.687437031435021e+70	-1.5421164969392891e+69	-8.946323817142764e+69
6	-4.951685707263575e+118	-5.329286401239366e+117	-5.454213675553863e+117

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	56	171
1	75	171
done	75	171

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.7s	2476×	body	1280	valid
2.7s	994×	body	2560	valid
1.3s	1654×	body	640	valid
736.0ms	3091×	body	80	valid
265.0ms	819×	body	320	valid
126.0ms	2201×	body	80	nan
72.0ms	433×	body	160	valid
26.0ms	5×	body	5120	valid